200mAh was the lowest I ever found. Was from an old LiIon power tool that was rated at 1000mah. Can still pull 7A from it without much problem. Was rated for 20-25A initially. Can't find a source for it though.
Now sitting in a triple AAA flashlight in case of small emergencies.

It's better to over engineer something than to cheap out.
As I say: You pay once, you cry once.
You pay multiple times, you are a doofus